Mesh opens at the back
As said in the comments, mirror modifier has to be 1st in the list (up), if it's not, click on the up arrow at the upper right corner of the mirror modifier. Be sure to check "merge" and "clipping" options.

If the problem still appears, edit your mesh, select all vertices that should be in the center. Scale them to zero (align) on the X axis (S X 0), then move them on X axis to make them stick (G X -move mouse-) repeat this on the other X direction (G X -move mouse to the other direction-). All center vertices should now be in the center, clipped and merged and will move with the armature as they should.